The existence and uniqueness of solutions for model (REF ) is not guaranteed in general. This is an innate property of the original Bradley-Terry model [1]}. As pointed out in [2]} existence of the MLE for the Bradley-Terry model parameters demands a sufficient amount of pairwise comparison data so that there is enough information of relative performance between any pair of two teams for parameter estimation purposes. For example, if there is a team which has never been compared to the others, there is no information which the model can exploit to assign a score for the team. As such its derived rank could be arbitrary. In addition if there are several teams which have never outperformed the others then the Bradley-Terry model would assign negative infinity for the performance of these teams. It would not be possible to compare amongst them for global ranking purposes. In all such cases, the model parameters are not estimable.
